/*Curve fitting problem by Least Squares

  Nigel_Galloway@operamail.com

  October 1st., 2007

*/

set Sample;

param Sx {z in Sample};

param Sy {z in Sample};

var X;

var Y;

var Ex{z in Sample};

var Ey{z in Sample};

/* sum of variances is zero for Sx*/

variencesX{z in Sample}: X + Ex[z] = Sx[z];

zumVariancesX: sum{z in Sample} Ex[z] = 0;

/* sum of variances is zero for Sy*/

variencesY{z in Sample}: Y + Ey[z] = Sy[z];

zumVariancesY: sum{z in Sample} Ey[z] = 0;

solve;

param b1 := (sum{z in Sample} Ex[z]*Ey[z])/(sum{z in Sample} Ex[z]*Ex[z]);

printf "\nbest linear fit is:\n\ty = %f %s %fx\n\n", Y-b1*X, if b1 < 0 then "-" else "+", abs(b1);

data;

param:

Sample:   Sx    Sy :=

  1         0    1

  2       0.5  0.9

  3         1  0.7

  4       1.5  1.5

  5       1.9    2

  6       2.5  2.4

  7         3  3.2

  8       3.5    2

  9         4  2.7

 10       4.5  3.5

 11         5    1

 12       5.5    4

 13         6  3.6

 14       6.6  2.7

 15         7  5.7

 16       7.6  4.6

 17       8.5    6

 18         9  6.8

 19        10  7.3

;

end;